Effects of numerical dispersion on pressure diffusion in CBM reservoirs

Abstract

The analysis of numerical dispersion in reservoir simulation usually focuses on its impacts on liquid saturation and component concentration profiles. However, the production of coalbed methane (CBM) reservoirs is highly sensitive to the pressure diffusion owing to its unique gas storage and flow mechanism. The effect of numerical dispersion on pressure diffusion during gas production has not been studied yet.In this work, the numerical dispersion term of pressure diffusion equation is derived using finite difference scheme to determine the influence of numerical dispersion on pressure diffusion. Simulation examples are then performed to evaluate the effect of numerical dispersion on pressure diffusion and gas production in CBM reservoirs. Finally, a field case is presented to study numerical dispersion impacts on gas rate, using the production history of two wells in Ordos Basin, China.The numerical dispersion term of pressure diffusion equation, derived in this paper, illustrates that the numerical dispersion is controlled by pressure diffusivity, grid size, time step and finite difference scheme. The simulation results indicate that both coarse grid and low permeability contribute to dramatic numerical dispersion and significant errors in simulation. Once the permeability is lower than 200 mD, there is a dramatic effect of grid size on numerical dispersion. A slight deviation of pressure still results in an unacceptable error in CBM production simulation. The simulation results and field example show that the numerical dispersion of pressure may overestimate the dewatering efficiency and gas production rate. An effective way to diminish the numerical dispersion in CBM reservoir simulation is to apply the fine grid system.